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The Naproche project 1 (NAtural language PROof CHEcking) studies the semi-formal language of mathematics (SFLM) as used in journals and textbooks from the perspectives of linguistics, logic and mathematics. A central goal of Naproche is to develop and implement a controlled natural language (CNL) for mathematical texts which can be transformed automatically(More)
We generalize standard Turing machines working in time ω on a tape of length ω to abstract machines with time α and tape length α, for α some limit ordinal. This model of computation determines an associated computability theory: α-computability theory. We compare the new theory to α-recursion theory, which was developed by G. Sacks and his school. For α an(More)
Using the core model K we determine better lower bounds for the consistency strength of some combinatorial principles: I. Assume that A is a Jonsson cardinal which is 'accessible' in the sense that at least one of (l)-(4) holds: (1) A is a successor cardinal; (2) A = oE and 6 <A ; (3) A is singular of uncountable cofinality; (4) A is a regular but not(More)
The Naproche project (Natural language Proof Checking) was initiated by Bernhard Schröder and Peter Koepke at the University of Bonn to focus on an interdisciplinary study of the semi-formal language of mathematics. A central goal of Naproche is to develop a controlled natural language (CNL) for mathematical texts and adapted proof checking software which(More)